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arXiv · 2306.07516

Weight hierarchies of 3-weight linear codes from two $p$-ary quadratic functions

Xiumei Li·Fei Li
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Abstract

The weight hierarchy of a linear code has been an important research topic in coding theory since Wei's original work in 1991. Choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+g(y)=0\Big\}$ as a defining set , where $f(x),g(y)$ are quadratic forms over $\mathbb{F}_{p^{s_i}},i=1,2$, respectively, with values in $\F_p$, we construct a family of 3-weight $p$-ary linear codes and determine their weight distributions and weight hierarchies completely. Most of the codes can be used in secret sharing schemes.

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Xiumei Li, Fei Li. 2023-06-13. Weight hierarchies of 3-weight linear codes from two $p$-ary quadratic functions. https://arxiv.org/abs/2306.07516

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